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Forum:Help with stating algorithm
I am playing around with an idea, and would like help with how to state a part of the algorithm as a mathmatical function. It's been a long time since I had a math class, so excuse any confusion but please clarify and correct. This is probably pretty trivial to answer one way or another. The part of the algorithm I want help with is: FISN(x) should be defined as a function that has x total nested levels of: the number x seperated by x conway chained arrows with the result iterated back into the preceding steps x times. To help clarify what I am trying to state here are some examples. FISN(0) = null >'s in 0 nested levels iterated 0 times FISN(1) = 1 > 1 [ 1's seperated by one >'s in one nested level(s) iterated one times] FISN(2) = Iteration 1: ((2 > 2 > 2) > (2 > 2 > 2) > (2 > 2 > 2)) = A So that's two >'s nested in two >'s filled with 2's. ::: Iteration 2: (... (A1 > A2 > ... > AA-1) > (A1 > A2 > ... > AA-1)... ) = x Where there are A nested levels of A number of >'s seporating the number A. seperated by two >'s in two nested levels with the those steps iterated a total of two times. Thus the answer from iteration one is the x for iteration two. *NOTE that includes defining the new level of nesting FISN(3) Iteration 1: (((3 > 3 > 3 > 3) > (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3)) > ((3 > 3 > 3 > 3) > (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3)) > ((3 > 3 > 3 > 3) > (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3)) > ((3 > 3 > 3 > 3) > (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3))) = A Where there are 3's seporated by three >'s nested three () deep in sets of three > operators. : Iteration 2: (... (A1 > A2 > ... > AA+1) > (A1 > A2 > ... > AA+1)... ) = B Where there are A nested levels of A number of >'s seporating the number A. : Iteration 3: (... (B1 > B2 > ... > BB+1) > (B1 > B2 > ... > BB+1)... ) Where there are B nested levels of B number of >'s seporating the number B. : seperated by three >'s in three nested levels with those steps iterated a total of three times. Thus the answer from iteration one is the x for iteration 2, and the answer from iteration two is the x for iteration 3